WOLFRAM|DEMONSTRATIONS PROJECT

Surfaces and Gradients

​
u
-3
v
-0.14
w
1.405
Visualize how gradients relate to surfaces.
The points
(x,y,z)
satisfying
w=f(x,y,z)=u
2
x
+v
2
y
+
2
z
for a particular value of
w
form the surface shown. As
w
varies, the surface deforms along the normals defined by the vector field
∇f=
∂f
∂x

i
+
∂f
∂y

j
+
∂f
∂z

k
, the gradient of
f
, represented by the arrows.
Due to the complex nature of this Demonstration, there may be a delay between changing the variables and updating the graph.